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CBSE Class 7 Mathematics — Ratios, Proportions and Percentages: complete chapter guide

CBSE Class 7 Mathematics Chapter 10 Ratios, Proportions and Percentages is where arithmetic meets everyday decision-making. Whether a parent is comparing mobile-plan offers, a student is calculating their test score percentage, or a shopkeeper is working out profit margins, the tools in this chapter are in constant use. NCERT Class 7 Mathematics structures this chapter to first build ratio fluency, then extend it to proportions for solving unknowns, and finally apply percentage calculations to money problems — profit, loss, discount, and simple interest. For CBSE Class 7 students, this chapter is not only scoring (it yields 12–15 marks in term exams) but also foundational: Class 8 compound interest, Class 9 linear equations in two variables, and Class 10 financial mathematics all build on Chapter 10. This guide unpacks every concept, formula, and worked example from the NCERT textbook, and shows parents and students exactly how to master CBSE Class 7 Mathematics Chapter 10 Ratios, Proportions and Percentages for both board exams and real life.

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Key takeaways

  • ✓CBSE Class 7 Mathematics Chapter 10 covers three interconnected concepts: ratios (comparing quantities), proportions (equating two ratios), and percentages (expressing ratios per hundred).
  • ✓Every ratio must be simplified to its simplest form by dividing both terms by their Highest Common Factor, exactly as prescribed in NCERT Class 7 Mathematics.
  • ✓The proportion rule — if a:b equals c:d, then a×d equals b×c — is the single most powerful tool for solving unknown values in Class 7 Mathematics Chapter 10.
  • ✓Profit percentage and loss percentage are always calculated on Cost Price, never on Selling Price, a rule repeatedly tested in CBSE Class 7 term exams.
  • ✓The simple interest formula SI equals (P×R×T) divided by 100 is non-negotiable; Amount always equals Principal plus SI, and students must memorize this for CBSE 7 Mathematics board papers.
  • ✓CBSE Class 7 Mathematics Chapter 10 Ratios, Proportions and Percentages typically carries 12–15 marks in term exams, with at least two long-answer questions on profit-loss or simple interest.
  • ✓Real-world applications — shopping discounts, bank interest, recipe scaling, speed-distance problems — all depend on fluency in CBSE Class 7 Mathematics Chapter 10 concepts.

What is a Ratio? Simplifying Ratios to Simplest Form (NCERT Class 7 Mathematics)

A ratio is a method of comparing two quantities of the same kind. When we say the ratio of boys to girls in a class is 5:3, we mean for every 5 boys there are 3 girls. Ratios are written as a:b and read as 'a to b', where a and b are called the terms of the ratio. The order matters: 5:3 is different from 3:5. Ratios can also be expressed as fractions — the ratio 5:3 means boys represent 5 parts out of a total of 8 parts (5 plus 3), so boys are 5÷8 of the total. Every ratio must be simplified to its simplest form by dividing both terms by their Highest Common Factor. For example, the ratio 12:8 has HCF equals 4, so it simplifies to 3:2. A ratio is in simplest form when the HCF of both terms is 1. This simplification rule is tested in every CBSE Class 7 Mathematics term exam. Students often lose marks by leaving ratios unsimplified — always check your final answer. Real-world example: A school has 60 footballs and 40 basketballs. The ratio is 60:40. The HCF is 20, so the simplified ratio is 3:2. This tells us that for every 3 footballs, there are 2 basketballs, regardless of the absolute numbers. Ratios are dimensionless — they compare relative sizes, not absolute quantities.
  • A ratio compares two quantities of the same kind, written as a:b.
  • Ratios must always be simplified by dividing both terms by their HCF.
  • A ratio is in simplest form when the HCF of both terms is 1.
  • Ratios can be expressed as fractions: a:b equals a÷(a plus b) for the first part.
  • Order matters: 5:3 is not the same as 3:5.

Understanding Proportions and the Cross-Multiplication Rule (CBSE Class 7 Mathematics Chapter 10)

A proportion is a statement that two ratios are equal. If a:b equals c:d, we say 'a is to b as c is to d', and this is a proportion. The four terms have special names: a and d are called extremes (the outer terms), and b and c are called means (the inner terms). The fundamental rule of proportions, taught in NCERT Class 7 Mathematics, is that the product of the means equals the product of the extremes. Mathematically: if a:b equals c:d, then a×d equals b×c. This cross-multiplication rule is your primary tool for solving proportion problems in CBSE Class 7 Mathematics Chapter 10 Ratios, Proportions and Percentages. If three terms of a proportion are known, you can always find the fourth by cross-multiplying. For example, if 5 notebooks cost Rs 150, how much do 12 notebooks cost? Set up the proportion: 5:150 equals 12:x. Cross-multiply: 5×x equals 150×12, so x equals 1800÷5 equals 360 rupees. This is called direct proportion — as one quantity increases, the other increases in the same ratio. The chapter also introduces inverse proportion (covered more deeply in Class 8), where one quantity increases as the other decreases, like speed and time for a fixed distance. Every CBSE Class 7 term exam includes at least two proportion problems, often worth 3 marks each. Students must write the proportion clearly, show cross-multiplication, and box the final answer.
  • A proportion states that two ratios are equal: a:b equals c:d.
  • Extremes are the outer terms (a and d); means are the inner terms (b and c).
  • The proportion rule: product of means equals product of extremes, so b×c equals a×d.
  • Cross-multiplication solves for any unknown term in a proportion.
  • Direct proportion: both quantities increase or decrease together.
  • Inverse proportion: one increases as the other decreases (introduced in this chapter, expanded in Class 8).

Percentage: Definition, Conversions, and Core Calculations (Class 7 Mathematics Chapter 10)

A percentage means 'per hundred' and is a way to express a ratio with denominator 100. The symbol is %. For example, 25% means 25 per hundred, which is 25÷100 equals 1÷4. Percentages make comparisons easy because they standardize different fractions to a common base of 100. If Class A has 30 out of 40 students passing and Class B has 60 out of 100 students passing, we convert to percentages: Class A is 75% and Class B is 60%, so Class A performed better. CBSE Class 7 Mathematics Chapter 10 Ratios, Proportions and Percentages requires fluency in four conversions. Percentage to decimal: divide by 100 (so 35% equals 0.35). Decimal to percentage: multiply by 100 (so 0.72 equals 72%). Percentage to fraction: write over 100 and simplify (so 40% equals 40÷100 equals 2÷5). Fraction to percentage: multiply by 100 (so 3÷5 equals 60%). Students lose marks by forgetting to simplify fractions or by writing 15% as 15 instead of 0.15 when calculating. Real example from NCERT Class 7 Mathematics: a shirt costs Rs 800 and is given a 20% discount. Discount amount equals 20% of 800 equals (20÷100)×800 equals 0.2×800 equals Rs 160. New price equals 800 minus 160 equals Rs 640. Percentage problems appear in every CBSE Class 7 term exam, often combined with profit-loss or simple interest.
  • Percentage means per hundred; 50% equals 50÷100 equals 1÷2.
  • Percentage to decimal: divide by 100.
  • Decimal to percentage: multiply by 100.
  • Percentage to fraction: write over 100, then simplify.
  • Fraction to percentage: multiply by 100.
  • Always convert percentage to decimal or fraction before multiplying.

Profit and Loss: Cost Price, Selling Price, and Percentage Calculations (CBSE 7 Mathematics)

When a shopkeeper buys an item for one price and sells it for another, the difference is either profit or loss. CBSE Class 7 Mathematics Chapter 10 Ratios, Proportions and Percentages defines four key terms. Cost Price (abbreviated CP) is the price at which an item is bought. Selling Price (abbreviated SP) is the price at which it is sold. Profit occurs when SP is greater than CP, and Profit equals SP minus CP. Loss occurs when SP is less than CP, and Loss equals CP minus SP. But raw profit or loss in rupees does not allow comparison across different items — a Rs 10 profit on a Rs 20 item is much better than a Rs 10 profit on a Rs 200 item. So we express profit and loss as percentages of the cost price. Profit percentage equals (Profit divided by CP) multiplied by 100. Loss percentage equals (Loss divided by CP) multiplied by 100. The denominator is always CP, never SP — this is a rule tested repeatedly in CBSE Class 7 term exams. Real example from NCERT: a fruit seller buys apples at Rs 40 per kg and sells them at Rs 50 per kg. CP equals Rs 40, SP equals Rs 50. Profit equals 50 minus 40 equals Rs 10. Profit percentage equals (10 divided by 40) multiplied by 100 equals 25%. Another example: a book costs Rs 200 to print and is sold for Rs 160. CP equals Rs 200, SP equals Rs 160. Loss equals 200 minus 160 equals Rs 40. Loss percentage equals (40 divided by 200) multiplied by 100 equals 20%. Every CBSE Class 7 Mathematics exam includes at least one 3-mark or 5-mark profit-loss problem.
  • Cost Price (CP) is the buying price; Selling Price (SP) is the selling price.
  • Profit equals SP minus CP (when SP is greater than CP).
  • Loss equals CP minus SP (when SP is less than CP).
  • Profit percentage equals (Profit divided by CP) multiplied by 100.
  • Loss percentage equals (Loss divided by CP) multiplied by 100.
  • Always use CP as the denominator, never SP.

Simple Interest Formula and Amount Calculation (NCERT Class 7 Mathematics)

Simple Interest is the extra money paid when you borrow or lend money. It is calculated only on the original sum, called the Principal, not on accumulated interest (that is called compound interest, which comes in Class 8). CBSE Class 7 Mathematics Chapter 10 Ratios, Proportions and Percentages introduces the SI formula: Simple Interest equals (P multiplied by R multiplied by T) divided by 100, where P is the Principal (the original amount in rupees), R is the Rate of interest per annum (per year, in percentage), and T is the Time in years. The Amount is the total money received or repaid, which equals Principal plus Simple Interest. Students must memorize this formula and the definitions of P, R, T, SI, and A — they appear in every CBSE Class 7 term exam, typically as a 4-mark or 5-mark question. Real example from NCERT: you deposit Rs 5000 in a bank at 8% per annum for 3 years. P equals 5000, R equals 8, T equals 3. SI equals (5000 multiplied by 8 multiplied by 3) divided by 100 equals 120000 divided by 100 equals Rs 1200. Amount equals 5000 plus 1200 equals Rs 6200. So your Rs 5000 grows to Rs 6200 after 3 years. Another example: a loan of Rs 2000 at 6% per annum for 2 years. SI equals (2000 multiplied by 6 multiplied by 2) divided by 100 equals 24000 divided by 100 equals Rs 240. Amount equals 2000 plus 240 equals Rs 2240. This is the total repayment. CBSE Class 7 students must show all steps clearly and box the final answer.
  • Simple Interest is calculated only on the Principal, not on accumulated interest.
  • SI formula: SI equals (P multiplied by R multiplied by T) divided by 100.
  • P is Principal (original sum in rupees).
  • R is Rate per annum (percentage per year).
  • T is Time in years.
  • Amount equals P plus SI (total money received or repaid).

Solving Multi-Step Proportion Problems in CBSE Class 7 Mathematics Chapter 10

Real-world problems in CBSE Class 7 Mathematics Chapter 10 Ratios, Proportions and Percentages often require chaining multiple steps — finding an unknown using proportion, then applying percentage or profit-loss formulae. For example, a CBSE term exam question might say: the ratio of flour to sugar in a recipe is 4:1. If 8 kg of flour is used, how much sugar is needed? If sugar costs Rs 50 per kg, what is the total cost? And if the shopkeeper sells the sugar at a 20% profit, what is the selling price per kg? Students must break this into steps. Step one: set up proportion. Flour:sugar equals 4:1 equals 8:x. Cross-multiply: 4x equals 8, so x equals 2 kg sugar. Step two: cost equals 2 multiplied by 50 equals Rs 100. Step three: profit equals 20% of 100 equals 0.2 multiplied by 100 equals Rs 20. SP equals 100 plus 20 equals Rs 120. Selling price per kg equals 120 divided by 2 equals Rs 60 per kg. NCERT Class 7 Mathematics emphasizes this stepwise problem-solving approach. Students must write clear intermediate steps, label quantities with units (kg, rupees, percentage), and box final answers. CBSE Class 7 board papers always include at least one such multi-step problem worth 5 marks. Teachers often tell students: 'Show your working, even if you get the wrong final answer, you can earn partial credit for correct steps.' Parents should ensure their child practices 10 to 15 such problems from the NCERT textbook and exemplar before term exams.
  • Multi-step problems combine ratios, proportions, and percentage calculations.
  • Always break the problem into clear steps and label each step.
  • Write intermediate answers with units (kg, rupees, %, years).
  • Use proportion to find unknown quantities, then apply profit-loss or SI formulae.
  • CBSE Class 7 exams reward clear working — partial credit is given for correct intermediate steps.
  • Practice NCERT textbook exercises 10.1 to 10.4 and exemplar problems for mastery.

Common Mistakes Students Make in CBSE Class 7 Mathematics Chapter 10 and How to Avoid Them

Every year, CBSE Class 7 students lose 20 to 30 marks in term exams by repeating the same errors in Chapter 10 Ratios, Proportions and Percentages. Here are the top mistakes and how to avoid them. Mistake one: writing 15% as 15 instead of 15÷100 or 0.15 when calculating. Always convert percentage to decimal or fraction before multiplying. Mistake two: calculating profit percentage or loss percentage using Selling Price as the denominator instead of Cost Price. The rule is non-negotiable: Profit percentage equals (Profit divided by CP) multiplied by 100, and Loss percentage equals (Loss divided by CP) multiplied by 100. Mistake three: forgetting to simplify a ratio. For example, leaving 20:30 instead of simplifying to 2:3. Always divide both terms by their HCF and write the simplest form. Mistake four: mixing up extremes and means in a proportion. Remember: in a:b equals c:d, the extremes are a and d, the means are b and c, and a multiplied by d equals b multiplied by c. Mistake five: using the wrong unit for time in the simple interest formula. The formula assumes time is in years. If a problem gives time in months, you must convert: 6 months equals 6÷12 equals 0.5 years. If time is in days, convert using 365 days per year. Mistake six: forgetting to add Principal and Simple Interest to find Amount. Many students calculate SI correctly but forget the final step: Amount equals P plus SI. CBSE Class 7 Mathematics teachers recommend that students maintain an error log — write down every mistake made in practice tests, the correct method, and revise this log weekly.
  • Always convert percentage to 0.01 multiplied by percentage before multiplying.
  • Profit percentage and loss percentage always use CP as denominator, never SP.
  • Simplify every ratio to simplest form by dividing both terms by HCF.
  • In proportions, extremes are outer terms, means are inner terms; cross-multiply correctly.
  • Convert time to years if given in months or days before using SI formula.
  • Amount always equals P plus SI; do not forget this final step.
  • Maintain an error log and revise it before CBSE Class 7 term exams.

Real-World Applications: Shopping, Banking, and Recipes (Class 7 Mathematics Chapter 10)

CBSE Class 7 Mathematics Chapter 10 Ratios, Proportions and Percentages is one of the most practically useful chapters in the entire NCERT curriculum because its concepts appear daily in real life. When parents compare mobile plans, they use ratios — Plan A offers 2 GB per day for Rs 300 per month, Plan B offers 3 GB per day for Rs 450 per month. Which is better value? Set up the ratio of GB to rupees for both and simplify to compare. When a student calculates their exam percentage — if you scored 432 out of 500, your percentage is (432÷500) multiplied by 100 equals 86.4%. When shopping during festival sales, a store advertises 30% off on a Rs 2000 jacket. The discount is 30% of 2000 equals 0.3 multiplied by 2000 equals Rs 600, so the sale price is 2000 minus 600 equals Rs 1400. Recipes use proportions constantly — if a recipe for 4 people needs 200g rice, how much rice for 10 people? Set up the proportion: 4:200 equals 10:x. Cross-multiply: 4x equals 2000, so x equals 500g rice. Banking uses simple interest — fixed deposits, loans, savings accounts all calculate interest using SI equals (P multiplied by R multiplied by T) divided by 100. A parent depositing Rs 50000 in a 3-year fixed deposit at 7% per annum earns SI equals (50000 multiplied by 7 multiplied by 3) divided by 100 equals Rs 10500, so the maturity amount is Rs 60500. NCERT Class 7 Mathematics includes many such real-world problems to show students that Chapter 10 is not abstract arithmetic but a toolkit for informed decision-making.
  • Mobile plans, internet plans, grocery pricing all use ratios for comparison.
  • Exam scores and school results are reported as percentages.
  • Shopping discounts, festival sales, cashback offers all use percentage calculations.
  • Recipes scale ingredients using proportions.
  • Banking products — fixed deposits, loans, savings accounts — calculate interest using simple interest formula.
  • CBSE Class 7 students who master Chapter 10 gain real financial literacy.

How CBSE Class 7 Mathematics Chapter 10 Connects to Higher Classes and Competitive Exams

CBSE Class 7 Mathematics Chapter 10 Ratios, Proportions and Percentages is foundational for Class 8, Class 9, and Class 10 board exams, as well as competitive exams like NTSE, Olympiads, and later JEE and CAT. In Class 8 NCERT Mathematics, Chapter 10 concepts extend to compound interest (where interest is calculated on principal plus accumulated interest), direct and inverse variation (formalizing direct and inverse proportions), and comparing quantities (percentage increase, percentage decrease, successive discounts, marked price versus selling price). In Class 9, linear equations in two variables often model proportion problems — if 3x plus 2y equals 12 and the ratio of x to y is 2:3, solve for x and y. In Class 10, financial mathematics builds on simple and compound interest, and statistics uses percentages to express frequency distributions and cumulative frequencies. Competitive exams love ratio-proportion problems because they test logical reasoning and proportional thinking. NTSE Stage 1 and Stage 2 Mental Ability Test includes problems like: if the ratio of boys to girls is 5:4 and 10 more boys join making the ratio 6:4, find the original number of students. IMO and NSO Olympiads test advanced percentage problems involving profit-loss chains, successive discounts, and mixture problems (mixing two liquids in a given ratio). Later, CAT quantitative aptitude has an entire section on ratios, proportions, and percentages, often combined with time-speed-distance or work-time problems. Students who build rock-solid mastery of CBSE Class 7 Mathematics Chapter 10 Ratios, Proportions and Percentages find these higher-level topics much easier. Parents should encourage daily practice of 5 to 10 problems from NCERT and reference books to build speed and accuracy.
  • Class 8 extends Chapter 10 to compound interest, direct and inverse variation, and comparing quantities.
  • Class 9 uses ratios and proportions in linear equations in two variables.
  • Class 10 applies simple and compound interest in financial mathematics.
  • NTSE, IMO, NSO Olympiads test advanced ratio-proportion reasoning.
  • CAT, JEE, and other competitive exams include entire sections on ratios, proportions, and percentages.
  • Daily practice of 5 to 10 NCERT problems builds speed and accuracy for higher classes and exams.

Chapter 10 Marking Scheme and Exam Strategy for CBSE Class 7 Mathematics Term Exams

CBSE Class 7 Mathematics Chapter 10 Ratios, Proportions and Percentages typically carries 12 to 15 marks in term exams, distributed across multiple question types. The marking scheme usually includes: two or three 1-mark multiple-choice or fill-in-the-blank questions testing definitions (e.g. 'What is the simplest form of 18:24?' or 'SI formula is ___'), two or three 2-mark short-answer questions requiring one-step calculations (e.g. 'Find 20% of 450' or 'Simplify the ratio 35:50'), two 3-mark questions involving profit-loss or proportion problems with two or three steps, and one 5-mark long-answer question combining multiple concepts (e.g. a multi-step problem involving ratio, proportion, and simple interest). CBSE Class 7 students should follow this exam strategy. First, revise all formulae the night before — write them on a single sheet and read it 10 times. Second, in the exam, attempt the 1-mark and 2-mark questions first to secure easy marks. Third, for 3-mark and 5-mark questions, write clear steps with labels — even if the final answer is wrong, you earn partial credit for correct intermediate steps. Fourth, always simplify ratios to simplest form and always write units (rupees, kg, %, years) next to numbers. Fifth, box or underline the final answer so the examiner can easily spot it. Sixth, if time permits, verify your answers — for proportion problems, check that both sides of the equation balance; for profit-loss, check that SP minus CP equals Profit; for simple interest, verify that Amount equals P plus SI. NCERT Class 7 Mathematics exemplar problems are the best resource for exam practice — solve all exemplar questions for Chapter 10 at least twice before term exams.
  • CBSE Class 7 Mathematics Chapter 10 typically carries 12 to 15 marks in term exams.
  • Question types: 1-mark MCQ or fill-in-the-blank, 2-mark short-answer, 3-mark medium, 5-mark long-answer.
  • Revise all formulae the night before and write them on a single revision sheet.
  • Attempt 1-mark and 2-mark questions first to secure easy marks.
  • Write clear steps with units and labels; partial credit is awarded for correct intermediate steps.
  • Always simplify ratios, write units, and box final answers.
  • Verify answers if time permits; use NCERT exemplar for practice.

How CBSETUTOR.ai Helps Students Master CBSE Class 7 Mathematics Chapter 10 Ratios, Proportions and Percentages

Many Class 7 students struggle with CBSE Class 7 Mathematics Chapter 10 Ratios, Proportions and Percentages because textbook explanations are terse and parents may not remember the cross-multiplication rule or the SI formula from their own school days. This is where CBSETUTOR.ai — India's first 24×7 AI tutor for CBSE Classes 6 to 12 — becomes invaluable. CBSETUTOR.ai has ingested every page of the NCERT Class 7 Mathematics textbook, exemplar, and sample papers, so it can explain any concept, formula, or worked example from Chapter 10 in simple language. If a student is stuck on NCERT Exercise 10.3 Question 7 (a multi-step proportion problem), they can upload a photo of the question to CBSETUTOR.ai, and the AI tutor will provide a step-by-step solution with clear explanations of where the proportion comes from, how to cross-multiply, and how to interpret the final answer. If a parent wants to check whether their child has simplified a ratio correctly, they can ask CBSETUTOR.ai 'Is 18:24 in simplest form?' and get an instant, accurate response. The AI tutor also generates unlimited practice problems similar to NCERT questions, so students can drill profit-loss percentage or simple interest calculations until fluency is automatic. CBSETUTOR.ai costs a flat ₹999 per month for all subjects, all classes (6 to 12), with a 3-day free trial and no credit card required. For parents who want their child to master CBSE Class 7 Mathematics Chapter 10 Ratios, Proportions and Percentages without expensive coaching classes or tutor fees, CBSETUTOR.ai is the most cost-effective and available-anytime solution. Students can ask questions at 10 pm while revising for a test the next morning, and the AI tutor responds instantly with NCERT-grounded, syllabus-accurate explanations.
  • CBSETUTOR.ai is a 24×7 AI tutor for CBSE Classes 6 to 12, covering all NCERT subjects.
  • It has ingested every NCERT Class 7 Mathematics textbook page, exemplar, and sample paper.
  • Students can upload a photo of any NCERT question and get a step-by-step solution.
  • The AI tutor explains concepts in simple language and generates unlimited practice problems.
  • Flat ₹999 per month for all subjects and all classes (6–12), with a 3-day free trial, no card required.
  • Parents can use CBSETUTOR.ai to check homework, clarify doubts, and reinforce Chapter 10 concepts at home.

Step-by-Step Solved Examples from NCERT Class 7 Mathematics Chapter 10

Worked examples are the best way to internalize the problem-solving techniques for CBSE Class 7 Mathematics Chapter 10 Ratios, Proportions and Percentages. Here are three detailed solutions modeled on NCERT exemplar problems. Example One (Ratio and Proportion Combined): In a school, the ratio of boys to girls is 5:3. If there are 250 boys, how many girls are there? Also, if every 5 students require 2 notebooks, how many notebooks are needed for all students? Solution Part A: Ratio of boys to girls equals 5:3. Number of boys equals 250. Let number of girls equals x. Set up proportion: 5:3 equals 250:x. Cross-multiply: 5 multiplied by x equals 3 multiplied by 250. So 5x equals 750. Therefore x equals 750 divided by 5 equals 150. Answer: There are 150 girls. Solution Part B: Total students equals 250 plus 150 equals 400. Ratio of students to notebooks equals 5:2. If 5 students need 2 notebooks, then 400 students need y notebooks. Set up proportion: 5:2 equals 400:y. Cross-multiply: 5 multiplied by y equals 2 multiplied by 400. So 5y equals 800. Therefore y equals 800 divided by 5 equals 160. Answer: 160 notebooks are needed. Example Two (Profit and Simple Interest): A shopkeeper buys a dozen pens for Rs 360. He sells each pen for Rs 35. Find his profit per pen and profit percentage. If he invests his total profit in a bank at 10% per annum for 2 years, how much interest does he earn? Solution Part A: Cost price of 12 pens equals Rs 360. Cost price per pen equals 360 divided by 12 equals Rs 30. Selling price per pen equals Rs 35. Profit per pen equals 35 minus 30 equals Rs 5. Profit percentage equals (Profit divided by CP) multiplied by 100 equals (5 divided by 30) multiplied by 100 equals 500 divided by 30 equals 16.67% (or 50 divided by 3 %). Answer: Profit per pen equals Rs 5, Profit percentage equals 16.67%. Solution Part B: Total profit for 12 pens equals 5 multiplied by 12 equals Rs 60. Principal (P) equals Rs 60. Rate (R) equals 10% per annum. Time (T) equals 2 years. SI equals (P multiplied by R multiplied by T) divided by 100 equals (60 multiplied by 10 multiplied by 2) divided by 100 equals 1200 divided by 100 equals Rs 12. Amount equals P plus SI equals 60 plus 12 equals Rs 72. Answer: Interest earned equals Rs 12, Total amount equals Rs 72.

Frequently asked questions

How many marks does CBSE Class 7 Mathematics Chapter 10 Ratios, Proportions and Percentages carry in term exams?+
CBSE Class 7 Mathematics Chapter 10 typically carries 12 to 15 marks in term exams, distributed across 1-mark MCQs, 2-mark short-answer questions, 3-mark medium problems, and one 5-mark long-answer question combining multiple concepts like ratio, proportion, profit-loss, or simple interest.
What is the simplest form of a ratio and why is it important in CBSE Class 7 Mathematics Chapter 10?+
A ratio is in simplest form when the Highest Common Factor (HCF) of both terms is 1. For example, 12:8 simplifies to 3:2 because HCF is 4. CBSE examiners deduct marks if students leave ratios unsimplified, so always divide both terms by their HCF and write the final answer in simplest form.
Why must profit percentage and loss percentage always be calculated on Cost Price, not Selling Price?+
Profit percentage and loss percentage are always calculated on Cost Price because that is the investment base. The formulae are Profit % equals (Profit divided by CP) multiplied by 100 and Loss % equals (Loss divided by CP) multiplied by 100. Using SP as the denominator would give incorrect comparisons and is marked wrong in CBSE Class 7 exams.
What is the cross-multiplication rule in proportions and how do I use it in CBSE Class 7 Mathematics Chapter 10?+
If a:b equals c:d, then a multiplied by d equals b multiplied by c. This is called the cross-multiplication rule. Use it to find an unknown term: if 5:150 equals 12:x, then 5x equals 150 multiplied by 12, so x equals 1800 divided by 5 equals 360. This rule solves every proportion problem in Chapter 10.
How do I convert a fraction to a percentage for CBSE Class 7 Mathematics Chapter 10 problems?+
Multiply the fraction by 100. For example, to convert 3 divided by 5 to a percentage, calculate (3 divided by 5) multiplied by 100 equals 0.6 multiplied by 100 equals 60%. So 3 divided by 5 equals 60%. This conversion is tested in almost every CBSE Class 7 term exam.
What is the simple interest formula and how do I remember the units for P, R, T in CBSE Class 7 Mathematics?+
The simple interest formula is SI equals (P multiplied by R multiplied by T) divided by 100. P is Principal in rupees, R is Rate per annum in percentage, T is Time in years. Remember: if time is given in months, convert to years by dividing by 12. Always write units next to your numbers in the exam to avoid confusion.
My child often forgets to add Principal and Simple Interest to find the Amount. How can I help them remember?+
Tell them: Amount is the total money you get back or pay back, so it must include both the original money (Principal) and the extra money (Simple Interest). The formula is Amount equals P plus SI. Make them write this formula at the top of every SI problem as a reminder. CBSETUTOR.ai also reinforces this step in every worked example.
How is CBSE Class 7 Mathematics Chapter 10 Ratios, Proportions and Percentages connected to Class 8 and Class 9 topics?+
In Class 8, Chapter 10 extends to compound interest, direct and inverse variation, and comparing quantities (marked price, discount, GST). In Class 9, ratio and proportion are used in linear equations in two variables and similarity of triangles. Mastery of CBSE Class 7 Mathematics Chapter 10 makes these higher topics much easier.
What are the most common mistakes students make in CBSE Class 7 Mathematics Chapter 10 and how can they avoid them?+
The top mistakes are: writing 15% as 15 instead of 0.15 when calculating, using SP instead of CP as the denominator for profit percentage, forgetting to simplify ratios, mixing up extremes and means in proportions, using months instead of years in the SI formula, and forgetting to add P plus SI to find Amount. Keep an error log and revise it weekly.
How many practice problems should my child solve to master CBSE Class 7 Mathematics Chapter 10 Ratios, Proportions and Percentages?+
Students should solve all NCERT textbook exercises (10.1 to 10.4), all NCERT exemplar problems for Chapter 10, and at least 50 additional problems from reference books or CBSETUTOR.ai. Daily practice of 5 to 10 problems for two weeks before term exams builds speed and accuracy. CBSETUTOR.ai generates unlimited similar problems for drilling.
Can CBSETUTOR.ai help if my child is stuck on a specific NCERT question from Chapter 10?+
Yes. Students can upload a photo of any NCERT question to CBSETUTOR.ai and get a step-by-step solution with clear explanations. The AI tutor has ingested every page of NCERT Class 7 Mathematics, so it provides syllabus-accurate, exam-ready answers. It is available 24×7, even at 10 pm the night before an exam, at a flat ₹999 per month for all subjects and classes 6 to 12.
Are there any mobile apps or online tools that help with practice for CBSE Class 7 Mathematics Chapter 10?+
CBSETUTOR.ai is the best 24×7 AI tutor for CBSE Classes 6–12, supporting photo upload of worksheets and generating unlimited practice problems for Chapter 10. It costs ₹999 per month (flat for all classes 6–12), with a 3-day free trial and no card required. Parents and students across India use it for instant doubt-solving and exam prep.

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